Abstract
A generalized definition of average, termed theq-average, is widely employed in the field of nonextensive statistical mechanics. Recently, ithas however been pointed out that such an average value may behave unphysically underspecific deformations of probability distributions. Here, the following three issues arediscussed and clarified. Firstly, the deformations considered are physical andmay be realized experimentally. Secondly, in view of the thermostatistics, theq-average is unstable in both finite and infinite discrete systems. Thirdly, a naive generalizationof the discussion to continuous systems misses a point, and a norm better than theL1-normshould be employed for measuring the distance between two probability distributions. Consequently, stabilityof the q-average is shown not to be established in all of the cases.
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